I was thinking of something along the same lines as an alliance (as you call it) bank but with at least 1 .ascension item in it for every titan defeated.
Everyone that fort that titan would get points based on there position and once a week or fortnight top 3 players would get to choose 1 item from that list. I feel/think as a different option to everything being random having a choice somewhere in the game would give players a fairer change at getting what they actually need.
As you said if a member leaves they lose there points and start again anew at next alliance.
This could work from 3 or 4 star titan upwards. An ascension item would be guaranteed with every titan for that allience.